Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Regents Exam Questions: Properties of Integers Name: ________________________ www.jmap.org Properties of Integers 1 If a and b are integers, which equation is always true? a b 1) b a 2) a 2b b 2a 3) a b b a 4) a b b a 7 Ramón said that the set of integers is not closed for one of the basic operations (addition, subtraction, multiplication, or division). You want to show Ramón that his statement is correct. For the operation for which the set of integers is not closed, write an example using: • a positive even integer and a zero • a positive and a negative even integer • two negative even integers Be sure to explain why each of your examples illustrates that the set of integers is not closed for that operation. 2 Which set is closed under division? 1) {1} 2) counting numbers 3) integers 4) whole numbers 8 If a is an odd number, b an even number, and c an odd number, which expression will always be equivalent to an odd number? 1) a(bc) 3 The set of integers is not closed for 1) division 2) multiplication 3) addition 4) subtraction 2) 3) 4) 4 Under which operation is the set of odd integers closed? 1) addition 2) subtraction 3) multiplication 4) division ac(b) 0 ac(b) 1 ac(b) 2 9 If a and b are both odd integers, which expression must always equal an odd integer? 1) a b 2) a b 3) a b a 4) b 5 Under which operation is the set {1,0,1} closed? 1) multiplication 2) division 3) addition 4) subtraction 10 If n represents an odd number, which computation results in an answer that is an even number? 1) 2 n 1 2) 2 n 1 3) 3 n 2 4) 3 n 1 6 Which statement is not true for the set of integers? 1) Every integer has an additive inverse. 2) Every integer has a multiplicative inverse. 3) The set of integers is closed under addition. 4) The set of integers is closed under multiplication. 1 ID: A Properties of Integers Answer Section 1 ANS: 4 The other equations are true only if a = b. REF: 010107a 2 ANS: 1 . (2)-(4) are not closed sets because whole numbers, REF: 010217a 3 ANS: 1 4 ANS: 3 and while 1 and 2 are counting numbers, integers and is not a counting number, integer or whole number. REF: 011523ia An odd plus and odd is even. An odd minus an odd is even. An odd divided by an odd can be a fraction. An odd times an odd is always odd. REF: 010928a 5 ANS: 1 REF: 060828a 6 ANS: 2 7 ANS: REF: 089335siii The set of integers is not closed under division. 2 0 • a positive even integer and a zero: 2 0 , which is not an integer 1 2 • a positive and a negative even integer: 2 4 , which is not an integer 1 2 • two negative even integers: 2 4 , which is not an integer REF: 080129a 8 ANS: 2 REF: 060113a 1 ID: A 9 ANS: 3 O O O REF: 060525a 10 ANS: 4 REF: 080113a 2